Transformation-Invariant Dictionary Learning for Classification with 1-Sparse Representations

Sparse representations of images in well-designed dictionaries can be used for effective classification. Meanwhile, training data available in most realistic settings are likely to be exposed to geometric transformations, which poses a challenge for the design of good dictionaries. In this work, we study the problem of learning class-representative dictionaries from geometrically transformed image sets. In order to efficiently take account of arbitrary geometric transformations in the learning, we adopt a representation of the dictionaries in an analytic basis. Then, the proposed algorithm learns atoms that are attracted to the samples of their own class while being repelled from the samples of other classes so that the discrimination between different classes is promoted. The dictionary learning objective is formulated such that it enhances the class-discrimination capabilities of individual atoms rather than the ones of the subspaces they generate, which renders the designed dictionaries especially suitable for fast classification of query images with very sparse approximations. Experimental results demonstrate the performance of the proposed method in handwritten digit recognition applications.